Frequency, Central Tendency & Variability

Frequency Distributions

  • FREQUENCY DISTRIBUTION
  • RELATIVE FREQUENCY DISTRIBUTION
  • PROPORTION
  • PERCENTAGE
  • CUMULATIVE
  • RATE
  • BAR GRAPH
  • HISTOGRAM
  • LINE GRAPH
  • STATISTICAL MAP

Objectives

  • Calculate proportions and percentages
  • Construct and analyze frequency, percentage, and cumulative distributions

DISTRIBUTION

Shows all the possible values (or intervals) of the data and how often they occur.


FREQUENCY DISTRIBUTION

A table reporting the number of observations falling into each category of the variable.

Table 1. Attitudes about sex before marriage

premarsx

n

always wrong

357

almost always wrong

122

wrong only sometimes

258

not wrong at all

1,378

Total

2,115

Survey question: There’s been a lot of discussion about the way morals and attitudes about sex are changing in this country. If a man and woman have sex relations before marriage, do you think it is _________.

Table 1. Attitudes about sex before marriage

premarsx

n

always wrong

357

almost always wrong

122

wrong only sometimes

258

not wrong at all

1,378

Total

2,115

The number of respondents who answered this survey question.

Table 1. Attitudes about sex before marriage

premarsx

n

always wrong

357

almost always wrong

122

wrong only sometimes

258

not wrong at all

1,378

Total

2,115

The number of respondents who said pre-marital sex was “wrong only sometimes.”

RELATIVE FREQUENCY DISTRIBUTION

A table showing the proportion or percentage for each value of a variable.


Proportions are between 0 and 1.0.

Proportion = count (f) / total number of cases (N).


Percentages are between 0 and 100.

Percentage = proportion × 100.

CUMULATIVE FREQUENCY DISTRIBUTION

The number or percentage of observations at or below a given category.


Table 3. Attitudes about sex before marriage, with cumulative percentages

premarsx

n

%

cumulative %

always wrong

357

17

17

almost always wrong

122

6

23

wrong only sometimes

258

12

35

not wrong at all

1,378

65

100

Total

2,115

100

175

\({\color{mathGreen} 17} + {\color{mathOrange} 6} = {\color{mathRed} 23\%}\)

RATES

\(\frac{Actual\;occurrences}{possible\;occurrences}\)


Examples:

Nominal variables:
can have frequency distributions, cannot have cumulative frequency distributions


Ordinal:
can have frequency distributions and cumulative frequency distributions


Interval-ratio:
can have frequency distributions, cumulative frequency distributions, and rates

A bar graph is used:
for nominal or ordinal variables,

to show frequencies or percentages,

using separated rectangles, with height proportional
to the frequency or percentage.

A histogram is used:
for interval-ratio variables,

to show frequencies or percentages,

using separated rectangles, with height proportional
to the frequency or percentage.

A line graph is used:
for interval-ratio variables,

to show frequencies or percentages,

joining by category the frequency or average with a line.

A statistical map is used:
for interval-ratio variables,

to show geographical variations, often in ratios,

using variation in color or hue.

Central Tendency